Efficient Computation of Physical Charging Free Energies for Monatomic Ions at Any Charge along Alchemical Charging Pathways.

One way to compute solvation free energies is through standard alchemical free energy (AFE) methods. But they can be expensive, and they do not give useful atomwise or site-specific decompositions. Alternatively, these challenges are partly addressed by bottom-up methods, like semi-explicit assembly (SEA), that start from atomic units and handle larger molecules using additivity rules. The latter methods require databases only on elementary monatomics. Here, we present an efficient strategy, λ-resolved free energy (λFE), to generate such databases. By resolving physical charging free energies at any intermediate charge state from a single alchemical free-energy simulation, λFE eliminates the need for separate alchemical charging calculations for atom types that differ only in their charge. This approach is significantly less costly and is robust across a range of charges, LJ parameters, system sizes, and three water models (TIP3P, TIP4P/EW, and TIP4P/2005). Combined with a cubic polynomial fit to the alchemical charging free energies, λFE yields a closed-form expression for absolute charging free energies of monatomic ions with any charge from a single alchemical simulation.